Reduce the concentrate by pouring thawed apple juice into a 5- to 6-quart pan. Boil rapidly, uncovered, until reduced to 1 1/4 cups, 4 to 8 minutes. Chill.
Rinse berries, drain dry and put into a 15 x 10-inch baking pan. If using strawberries, slice them. Mix fruit and reduced concentrate and bake uncovered in a 375° F oven until berries release juice, about 10 minutes.
Meanwhile, put a ceramic saucer in the freezer. Reduce oven temperature to 325. Every 20 minutes or so, gently stir berries to moisten well with juice. Bake until a little berry liquid spooned onto a chilled saucer doesn't flow together when you pull the tip of a spoon or your fingertip through it (as you lift the spoon or your finger, the liquid holds on, forming a small droplet).
This should take about 1 hour for blueberries and 1 to 1 1/2 hours for other berries. Let jam cool; if necessary, reheat and adjust consistency. Spoon into bowl or small jars. Serve, or cover airtight and chill up to 2 weeks.Servings: 1-1/2 cups